This is the most comprehensive survey of the mathematical life of the legendary Paul Erdős (1913-1996), one of the most versatile and prolific mathematicians of our time. For the first time, all the main areas of Erdős' research are covered in a single project. Because of overwhelming response from the mathematical community, the project now occupies over 1000 pages, arranged into two volumes. These volumes contain both high level research articles as well as key articles that survey some of the cornerstones of Erdős' work, each written by a leading world specialist in the field. A special chapter "Early Days", rare photographs, and art related to Erdős complement this striking collection. A unique contribution is the bibliography on Erdős' publications: the most comprehensive ever published. This new edition, dedicated to the 100th anniversary of Paul Erdős' birth, contains updates on many of the articles from the two volumes of the first edition, several new articles from prominent mathematicians, a new introduction, more biographical information about Paul Erdős, and an updated list of publications.
The first volume contains the unique chapter "Early Days", which features personal memories of Paul Erdős by a number of his colleagues. The other three chapters cover number theory, random methods, and geometry. All of these chapters are essentially updated, most notably the geometry chapter that covers the recent solution of the problem on the number of distinct distances in finite planar sets, which was the most popular of Erdős' favorite geometry problems.
Author(s): Béla Bollobás (auth.), Ronald L. Graham, Jaroslav Nešetřil, Steve Butler (eds.)
Edition: 2
Publisher: Springer-Verlag New York
Year: 2013
Language: English
Pages: 563
Tags: Mathematics, general; Number Theory; Convex and Discrete Geometry; Probability Theory and Stochastic Processes
Front Matter....Pages i-xix
Paul Erdős: Life and Work....Pages 1-41
Erdős Magic....Pages 43-46
Front Matter....Pages 47-49
Some of My Favorite Problems and Results....Pages 51-70
Integers Uniquely Represented by Certain Ternary Forms....Pages 71-79
Did Erdős Save Western Civilization?....Pages 81-92
Encounters with Paul Erdős....Pages 93-98
On Cubic Graphs of Girth at Least Five....Pages 99-101
Front Matter....Pages 103-106
Cross-Disjoint Pairs of Clouds in the Interval Lattice....Pages 107-117
Classical Results on Primitive and Recent Results on Cross-Primitive Sequences....Pages 119-132
Dense Difference Sets and Their Combinatorial Structure....Pages 133-146
Integer Sets Containing No Solution to $$x + y = 3z$$ ....Pages 147-157
On Primes Recognizable in Deterministic Polynomial Time....Pages 159-186
Ballot Numbers, Alternating Products, and the Erdős-Heilbronn Conjecture....Pages 187-205
On Landau’s Function g ( n )....Pages 207-220
On Divisibility Properties of Sequences of Integers....Pages 221-232
On Additive Representative Functions....Pages 233-262
Arithmetical Properties of Polynomials....Pages 263-267
Some Methods of Erdős Applied to Finite Arithmetic Progressions....Pages 269-287
Sur la non-dérivabilité de fonctions périodiques associées à certaines formules sommatoires....Pages 289-300
1105: First Steps in a Mysterious Quest....Pages 301-308
Front Matter....Pages 309-309
Games, Randomness and Algorithms....Pages 311-342
On Some Hypergraph Problems of Paul Erdős and the Asymptotics of Matchings, Covers and Colorings....Pages 343-369
The Origins of the Theory of Random Graphs....Pages 371-397
An Upper Bound for a Communication Game Related to Time-Space Tradeoffs....Pages 399-407
How Abelian is a Finite Group?....Pages 409-423
On Small Size Approximation Models....Pages 425-433
The Erdős Existence Argument....Pages 435-444
Front Matter....Pages 445-446
Extension of Functional Equations....Pages 447-459
Remarks on Penrose Tilings....Pages 461-481
Distances in Convex Polygons....Pages 483-492
Unexpected Applications of Polynomials in Combinatorics....Pages 493-522
The Number of Homothetic Subsets....Pages 523-532
On Lipschitz Mappings Onto a Square....Pages 533-540
A Remark on Transversal Numbers....Pages 541-549
In Praise of the Gram Matrix....Pages 551-557
On Mutually Avoiding Sets....Pages 559-563
